Show commands:
SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 12675.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12675.v1 | 12675bc1 | \([0, 1, 1, 867, 13394]\) | \(2097152/3375\) | \(-115857421875\) | \([]\) | \(10368\) | \(0.80812\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12675.v1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12675.v do not have complex multiplication.Modular form 12675.2.a.v
sage: E.q_eigenform(10)